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For searching and detecting near-field unknown ferromagnetic targets, four automatic search algorithms are proposed based on magnetic anomaly information from any position on planes or in space. Firstly, gradient search algorithms and enhanced gradient search algorithms are deduced using magnetic modulus anomaly information and magnetic vector anomaly information. In each algorithm, there are plane search forms and space search forms considering different practical search situations. Then the magnetic anomaly space data of typical magnetic source of oblique magnetization are forwardly simulated by ANSYS MAXWELL software. The plane distributions of some variables are numerically computed and the search destinations of different algorithms are predicted. Four automatic search algorithms are applied to simulate search paths on three characteristic orthogonal planes and in whole solution space. The factor affecting the performance of algorithms is analyzed. Features of each algorithm in different conditions are analyzed and suitable applications are discussed and verified by the experiment. The results show that proposed search algorithms require few prior information and have real-time performance for searching and tracking magnetic anomaly target.

With the development of magnetic signal processing technology [

According to objects’ features, there are two types of technologies for MAD. One considers the magnetic dipole model as the excitation source and the localization of magnetic dipole has been widely investigated in many cases, especially in submerged targets such as solid buried targets [

The other type technology of MAD concentrates on the detection of large-scale area with complex magnetic anomaly distribution which is mainly applied in mineral exploration and geologic mapping of prospective areas with buried igneous bodies. This kind of studies relies on magnetic inversion and quantitative interpretation [

Limited by the hypothesis of magnetic dipole model, the first technology can only detect and track targets in a long distance so that it cannot be applied for the targets in near-field. The second method which acquires the whole magnetic field data in advance restricts its real-time application. Therefore, limited by shortcomings of existing methods, they can only realize locating targets and it is the first time that the magnetic anomaly information is employed in automatic search. In this paper, we focus on the situation when the magnetic measuring system is near a big-scale ferromagnetic target, which determines that the magnetic dipole model is no longer applicable. Four automatic search algorithms based on local magnetic anomaly information are proposed, which can be applied to search from any point on planes or in space without knowing the features of the target and the space magnetic anomaly data in advance. Comparing with the two types of technologies above, four different algorithms applied in automatic searching near-field unknown ferromagnetic targets we proposed require few prior information and have real-time performance for searching and tracking magnetic anomaly targets.

The remainder of this paper is organized as follows. In Section

Consider measuring the magnetic anomaly vector

The main prospecting instruments such as proton magnetometers and optically pumped magnetometers measure the magnitude of

According to the analysis of relations among vectors

From (

The continuous form of magnetic field gradients is expressed by (

The discrete form of gradients along the edges is similar to interior gradient. The distinction is to calculate the difference with the adjacent node and the calculation process is omitted.

In order to search for some underwater or buried targets, plane search is an important approach and needs to be studied. Choose

The gradient unit vectors of MMA and MVA at point

Then two kinds of automatic plane search algorithms based on magnetic anomaly gradients can be described as

If

Accordingly, (

In order to interpret magnetic anomaly field information better, enhanced gradients are derived from magnetic anomaly gradient modulus. Similarly, considering the

The discrete form of the interior enhanced gradients in

The discrete form of gradients along the edges is similar to interior gradient. The distinction is to calculate the difference with the adjacent node and the calculation process is omitted.

As for any point

The enhanced gradient unit vectors of MMA and MVA at point

Then two kinds of automatic plane search algorithms based on magnetic anomaly enhanced gradients can be defined as

Likewise, (

Accordingly, plane search algorithms described by (

We firstly simulate the space magnetic anomaly field distribution of a typical object. A cubic solution space with length = 1000 m established by ANSYS MAXWELL shows in Figure

Magnetic anomaly simulation model and solution space.

By analyzing the simulated data of magnetic anomaly outside the cuboid object, it is found that the distribution laws are consistent separately with three groups of orthogonal planes parallel to

According to (

Distributions of magnetic anomaly on characteristic orthogonal planes. (a)-(c) Distributions of MMA on planes of

Likewise, distributions of

Distributions of plane gradient modulus of magnetic anomaly on characteristic orthogonal planes. (a)-(c) Distributions of plane gradient modulus of MMA on planes of

Automatic plane searches are also conducted on characteristic orthogonal planes of

As shown in Figure

Automatic plane search paths based on gradient of magnetic anomaly. (a)-(c) Automatic search paths based on gradient of MMA on planes of

Automatic space searches are conducted in the solution space. There are 25, 24, and 25 initial search points uniformly distributed on plane

Automatic space search paths based on gradient of magnetic anomaly. (a) Automatic space search paths based on gradient of MMA; (b) automatic space search paths based on gradient of MVA; (c)-(e) top view, side view, and front view of figure (a); (f)-(h) top view, side view, and front view of figure (b).

With the same initial search points condition, plane search paths are calculated by (

Automatic plane search paths based on enhanced gradient of magnetic anomaly. (a)-(c) Automatic search paths based on enhanced gradient of MMA on planes of

Figure

Automatic space search paths based on enhanced gradient of magnetic anomaly. (a) Automatic space search paths based on enhanced gradient of MMA; (b) automatic space search paths based on enhanced gradient of MVA; (c)-(e) top view, side view, and front view of figure (a); (f)-(h) top view, side view, and front view of figure (b).

The simulation conditions is the same as Section

Automatic space search paths based on gradient of magnetic anomaly with a geomagnetic field direction along the vector n=(√2,1,-1). (a) Automatic space search paths based on gradient of MMA; (b) automatic space search paths based on gradient of MVA; (c)-(e) top view, side view, and front view of figure (a); (f)-(h) top view, side view, and front view of figure (b).

Automatic space search paths based on enhanced gradient of magnetic anomaly with a geomagnetic field direction along the vector n=(√2,1,-1). (a) Automatic space search paths based on enhanced gradient of MMA; (b) automatic space search paths based on enhanced gradient of MVA; (c)-(e) top view, side view, and front view of figure (a); (f)-(h) top view, side view, and front view of figure (b).

Comparing the results of four plane searches in Figures

Comparing the results of four space searches in Figures

Comparisons of four automatic search algorithms.

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| Plane: partly converge | Plane: partly converge | Plane: all converge | Plane: all converge |

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| Plane: longest | Plane: longer | Plane: shorter | Plane: shortest |

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| Plane: certain points | Plane: certain points or around projection profiles | Plane: certain points | Plane: around projection profiles |

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| Preliminary detection | Search and tracking with low cost | Precise and efficient search and tracking | Plane boundary search and identification |

However, when applying algorithms to real engineering tasks, some technological limitations need to be considered. For example, the attitude change of mobile magnetic sensors system critically affects the measurement precision of magnetic field vector which affects the precision of MVA, thereby increasing the ambiguity of searching direction. So the measurement of MVA is much more difficult and has higher requirements on measuring instruments. What is more, the coupling effect of the high-order derivative and the noise of sensors can also influence the application of enhanced gradient algorithms. By considering these factors, suitable applications are discussed for each algorithm. Firstly, it is simplest to implement based on gradient algorithm of MMA while the search results are of the worst. It can satisfy the preliminary detection. Considering the improvement of enhanced gradient algorithm of MMA, it is more suitable to search and track for target with relative low cost. As for algorithms based on MVA, gradient algorithm is the most precise and efficient approach for search and tracking. Finally, the most advantages of enhanced gradient algorithm of MVA are plane boundary search and identification.

To verify the practicability and effectiveness of algorithms proposed, an experiment is designed. Figure

Experiment devices.

The magnetizing direction is the same as Section

Automatic space search paths based on gradient and enhanced gradient of MMA running in real magnetic field. (a) Automatic space search paths based on gradient of MMA; (b) automatic space search paths based on enhanced gradient of MMA; (c)-(e) top view, side view, and front view of figure (a); (f)-(h) top view, side view, and front view of figure (b).

Automatic space search paths based on gradient and enhanced gradient of MVA running in real magnetic field. (a) Automatic space search paths based on gradient of MVA; (b) automatic space search paths based on enhanced gradient of MVA; (c)-(e) top view, side view, and front view of figure (a); (f)-(h) top view, side view, and front view of figure (b).

We have proposed four automatic search algorithms based on searching and tracking near-field magnetic anomaly targets. By measuring information of magnetic modulus anomaly or magnetic vector anomaly from any point, automatic search can be conducted on planes or in space. To study these algorithms, typical magnetic anomaly distributions are forwardly simulated. Then the magnetic field data on characteristic orthogonal planes and in solution space are extracted and search simulations are carried out. Next, the effects and features of each algorithms are analyzed and compared. Finally, an experiment is present to verify algorithms in real magnetic fields. To overcome the limitation of methods based on magnetic dipole model [

We have proposed four different algorithms based on the magnetic anomaly information to realize automatic search to near-field ferromagnetic targets and it is the first time that the magnetic anomaly information is used in automatic search. There are still some improved spaces:

The computational method of gradient is the simplest form. The performance of algorithms could be improved by changing the gradient form to shorten the path and accelerate converge speed.

Theoretically, algorithms proposed can be applied to moving objects. More simulation and experiment are expected to verify.

The measurement of

All the data used in the article are simulated in ANSYS Maxwell and algorithms are implemented by Matlab. Magnetic field models and codes of algorithms are available if you email the authors.

The authors declare that we have no conflicts of interest.